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%I M2198 N0876 #17 Dec 26 2016 02:01:46
%S 0,0,3,0,5,-3,7,-8,3,-15,22,-15,39,-35,38,-72,85,-111,152,-175,241,
%T -308,414,-551,655,-897,1164,-1463,2001,-2538,3286,-4296,5503,-7259,
%U 9357,-12147,15910,-20406,26640,-34703,44854,-58481,75809,-98340
%N a(1) = 0, a(2) = 0; for n > 2, a(n) - a(n-3) - a(n-5) - ... - a(n-p) = n if n is prime, otherwise = 0, where p = largest prime < n.
%C Arises in studying the Goldbach conjecture.
%D P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. [Coll. Papers, Vol. II, pp. 354-382] [The sequence f_n]
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002123/b002123.txt">Table of n, a(n) for n = 1..1000</a>
%H P. A. MacMahon, <a href="http://plms.oxfordjournals.org/content/s2-23/1/290.extract">Properties of prime numbers deduced from the calculus of symmetric functions</a>, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380.
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%o (Haskell)
%o import Data.List (genericIndex)
%o a002123 n = genericIndex a002123_list (n - 1)
%o a002123_list = 0 : 0 : f 3 where
%o f x = y : f (x + 1) where
%o y = a061397 x -
%o sum (map (a002123 . (x -)) $ takeWhile (< x) a065091_list)
%o -- _Reinhard Zumkeller_, Mar 21 2014
%Y Cf. A065091, A061397.
%K sign
%O 1,3
%A _N. J. A. Sloane_
%E Extended with signs by _T. D. Noe_, Dec 05 2006
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